integral from 0 to 5 of 5x^2-x^3

解

\int_{0}^{5} 5 x^{2} - x^{3} d x

\frac{625}{12}

十進法表記

52.08333 \dots

解答ステップ

\int_{0}^{5} 5 x^{2} - x^{3} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} 5 x^{2} d x - \int_{0}^{5} x^{3} d x

\int_{0}^{5} 5 x^{2} d x = \frac{625}{3}

\int_{0}^{5} x^{3} d x = \frac{625}{4}

= \frac{625}{3} - \frac{625}{4}

簡素化

\frac{625}{3} - \frac{625}{4} : \frac{625}{12}

= \frac{625}{12}